$ \text{The number of points where the function } f:\mathbb{R}\to\mathbb{R},\quad f(x)=|x-1|\cos|x-2|\sin|x-1|+(x-3),|x^{2}-5x+4|,\ \text{is NOT differentiable, is:} $

1

$ \text{Let the focal chord of the parabola } P: y^{2}=4x \text{ along the line } L: y=mx+c,; m>0 \text{ meet the parab…

Topic: JEE Main 2022 (29 July Morning Shift)

2

The area of the region$\left\{(x, y):|x-1| \leq y \leq \sqrt{5-x^{2}}\right\}$ is equal to :

Topic: JEE Main 2022 (29 July Morning Shift)

3

The area of the region$\left\{(x, y):|x-1| \leq y \leq \sqrt{5-x^{2}}\right\}$ is equal to :

Topic: JEE Main 2022 (29 July Morning Shift)

4

If $f(\alpha)=\int\limits_{1}^{\alpha} \frac{\log _{10} \mathrm{t}}{1+\mathrm{t}} \mathrm{dt}, \alpha>0$ then $f\left(\…

Topic: JEE Main 2022 (29 July Morning Shift)

5

Let $\hat{a}$ and $\hat{b}$ be two unit vectors such that the angle between them is $\frac{\pi}{4}$. If $\theta$ is the…

Topic: JEE Main 2022 (29 July Morning Shift)

6

Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1,1). If the line AP interse…

Topic: JEE Main 2022 (29 July Morning Shift)

7

Let a line L pass through the point of intersection of the lines $b x+10 y-8=0$ and $2 x-3 y=0, \mathrm{~b} \in \mathbf…

Topic: JEE Main 2022 (29 July Morning Shift)

8

$ \text{Let the solution curve } y=y(x) \text{ of the differential equation } (1+e^{2x})!\left(\dfrac{dy}{dx}+y\right)=…

Topic: JEE Main 2022 (29 July Morning Shift)

9

Let the solution curve $y = y(x)$ of the differential equation $\left(1 + e^{2x}\right)\left(\dfrac{dy}{dx} + y\right) …

Topic: JEE Main 2022 (29 July Morning Shift)

10

The integral $\int_{0}^{\tfrac{\pi}{2}} \dfrac{1}{3 + 2 \sin x + \cos x} , dx$ is equal to :

Topic: JEE Main 2022 (29 July Morning Shift)

1

$ \text{The number of points where the function } f:\mathbb{R}\to\mathbb{R},\quad f(x)=|x-1|\cos|x-2|\sin|x-1|+(x-3),|x…

Topic: JEE Main 2022 (29 July Morning Shift)

2

$ \text{Let } f(x)=3^{(x^{2}-2)^{3}+4},; x\in\mathbb{R}. \text{ Then which of the following statements are true?} $ $P:…

Topic: JEE Main 2022 (29 July Morning Shift)